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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Grade 7 - Mathematics
8.4 Problems on Quadrilaterals - III

  1. Example:
    The angles of a quadrilateral are x, x-10, x+30 and 2x. Find the angles.

    Solution:
    We know that the sum of the four angles of any quadrilateral is 360.
    So, x + (x-10) + (x+30) + 2x = 360
    x + x - 10 + x + 30 + 2x = 360
    5x + 20 = 360
    5x = 360 - 20
    5x = 340
    x = 340/5
    x = 68
    Substituting x value, we get
    68, 58, 98 and 136.

  2. Example:
    In a quadrilateral, the first angle is 7 more than the second, 3 less than the third and 5 times the fourth. Find the angles?

    Solution:
    Let the first angle be 'x'. Then the second angle will be 'x + 7'.
    The third angle and fourth angle will be 'x - 3' and '5x' respectively.
    Since the sum of the angles of a quadrilateral is 360;
    we have x + x + 7 + x - 3 + 5x = 360;
    ie 8x + 4 = 360;
    ie 8x = 360 - 4 = 296;
    ie x = 296/8 = 37.
    Therefore first angle = 37, second angle = 44, third angle = 34 and fourth angle = 185

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Directions: Read the above example carefully and answer the following questions:
  1. In a quadrilateral, the first angle is 2 times the second, the remaining two angles are 5 more than the first. What is the measure of each of these angles?
  2. In a quadrilateral, the first angle is 6 times the second, 9 more than the third and 5 less than the fourth. What is the measure of each of these angles?

Q 1: The angles of a quadrilateral are x, x+5, x+10 and 2x. Find the second and fourth angles.
59 and 148 respectively.
74 and 138 respectively.
85and 140 respectively.
86 and 128 respectively.

Q 2: The angles of a quadrilateral are x, x+15, x-5 and 2x. Find the first and third angles.
70 and 65 respectively.
69 and 79 respectively.
74 and 79 respectively.
62 and 92 respectively.

Question 3: This question is available to subscribers only!

Question 4: This question is available to subscribers only!


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